The paper introduces the concept of non-interactive zero-knowledge proofs, demonstrating that interaction in zero-knowledge proofs can be replaced by sharing a common, short, random string. This result is used to construct the first public-key cryptosystem secure against chosen ciphertext attacks. The authors show that computational difficulty is the key ingredient in zero-knowledge proofs, and that interaction and hidden randomization are not essential. They provide a detailed formalization of the notion, including definitions, complexity assumptions, and protocols for single-theorem and non-interactive zero-knowledge proofs. The paper also discusses the robustness of the result and its applications, particularly in cryptography.The paper introduces the concept of non-interactive zero-knowledge proofs, demonstrating that interaction in zero-knowledge proofs can be replaced by sharing a common, short, random string. This result is used to construct the first public-key cryptosystem secure against chosen ciphertext attacks. The authors show that computational difficulty is the key ingredient in zero-knowledge proofs, and that interaction and hidden randomization are not essential. They provide a detailed formalization of the notion, including definitions, complexity assumptions, and protocols for single-theorem and non-interactive zero-knowledge proofs. The paper also discusses the robustness of the result and its applications, particularly in cryptography.